Zingers

Date: 11/06/2002 at 13:25:10
From: Kathi Stanley
Subject: Numbers - Zingers
The question is from an extra credit family brain teaser for my 5th
grader:
The following numbers are zingers:
9,41,57,73,17,89,33
The following numbers are not zingers:
7,22,45,8,59,36,68,13
Which of the numbers below are zingers?
4,55,63,25,49,24,77,92,38,42,20,65
We've tried to come up with a pattern, but just can't figure it out.
We'd all greatly appreciate any help you can provide. Thanks so much!

Date: 11/06/2002 at 14:12:22
From: Doctor Greenie
Subject: Re: Numbers - Zingers
Hello, Kathi -
"Zinger" is not part of standard mathematical terminology, but
sometimes a teacher will make up a term like 'zinger' in the course of
a lesson about identifying patterns.
It should help if you put the given list of zingers in numerical
order:
9, 17, 33, 41, 57, 73, 89
These numbers by themselves probably don't suggest a pattern or a
common trait for zingers. But let's look at the differences between
the zingers we have:
9 17 33 41 57 73 89
8 16 8 16 16 16
The differences between the zingers we have are all multiples of 8;
this means that the difference between any two zingers is a multiple
of 8. Because the difference between any two zingers is a multiple
of 8, the common trait that zingers have is that they all leave the
same remainder when divided by 8.
So now you can examine the other candidates to see which numbers are
zingers and which are not.
I hope this helps. Please write back if you have any further
questions about this.
- Doctor Greenie, The Math Forum
http://mathforum.org/dr.math/